In an experimental setting where a categorical response has to be given, the same response can, in theory, be generated by different latent processes. For example, in an experiment where participants have to indicate whether a particular word was part of a word list they learned earlier, some correct responses may be based on actual recollection of the word, and some may be due to guessing.
Based on the proportions of certain responses in different conditions, multinomial process models allow one recover the occurrence probabilities of these latent processes. However, different latent processes may be associated with different response latencies. Is there an extension of multinomial process models that takes response latencies into account, and if so, is there software for doing that?